The chaos in the synchrony of abnormal oscillations in a pair of neurons coupled via gap junction

The synchrony of abnormally excitable neurons is a hallmark in epileptic seizure. In order to study the nonlinear oscillations in two neurons coupled via gap junction in epilepsy, the model of a pair of neurons is derived from Chay model that gives many kinds of abnormal oscillations in excitable neurons by three nonlinear variables dynamics equations. The synchrony between two electrically coupled excitable neurons is found and a theoretical effort is carried out to investigate the chaos in the synchronous oscillations of the membrane potentials by the Lyapunov exponent and the phase portrait. It is shown that synchronous abnormal oscillations of membrane potentials can occur when the coupling strength of gap junction is large enough and the concentration of Ca² ions does not synchronize while the membrane potentials are synchronous and the coupling mechanism is chaotic. It is concluded that the synchrony and the chaos make birth to the new oscillations while disorder process such as epileptic seizure. The theoretical analysis may be helpful to investigate the mechanism of synchrony and the relationship between abnormal oscillations and gap junctions from nonlinear oscillatory points of view.